Average Error: 0.2 → 0.2
Time: 4.7s
Precision: 64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
↓
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r866683 = x;
        double r866684 = 16.0;
        double r866685 = 116.0;
        double r866686 = r866684 / r866685;
        double r866687 = r866683 - r866686;
        double r866688 = 3.0;
        double r866689 = r866687 * r866688;
        double r866690 = y;
        double r866691 = r866689 * r866690;
        return r866691;
}
↓
double f(double x, double y) {
        double r866692 = x;
        double r866693 = 16.0;
        double r866694 = 116.0;
        double r866695 = r866693 / r866694;
        double r866696 = r866692 - r866695;
        double r866697 = 3.0;
        double r866698 = r866696 * r866697;
        double r866699 = y;
        double r866700 = r866698 * r866699;
        return r866700;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

  2. Final simplification0.2

    \[\leadsto \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))